An object (any object) is dropped from a height of 300m
How long does it take this object to fall to the ground?
h = dy = ½ * 10 * t2 = 300
300 * 2 / 10 = t2 = 60
t = 7.75 s
Compare this answer with you answer from question 1, part c). What are the reasons for any similarities or differences?
They are the same. This is because their vertical motions are identical. All objects fall with the same gravitational acceleration, so two objects at the same height with the same initial vertical velocity will reach the ground at the same time.
The intent of a bean bag toss game is to get your bean bag to land on the ‘bull’s-eye’ of a target. The target is set up parallel to the ground and is the same height above the ground as your hand is when you let go of the bean bag. The game’s rules further require you to be 5 m from the center of the target when you release the bag.
Evaluate the following questions for both an angle of 32o and an angle of 58o if the bean bag is thrown with an initial velocity of 6 m/s:
What are the components of velocity?
Vx32: Cos 32o = Vx32/6 Vx58: Cos 58o = Vx58/6
6 * Cos 32o = Vx32 = 5.09 m/s 6 * Cos 58o = Vx58 = 3.18 m/s
Vy32: Sin 32o = Vy32/6 Vy58: Sin 58o = Vy58/6
6 * Sin 32o = Vy32 = 3.18 m/s 6 * Sin 58o = Vy58 = 5.09 m/s
What is the maximum height of the bean bag’s motion?
If the center of the bull’s-eye ranges from 4.9 m to 5.1 m away from you, does your bean bag win?
A stunt driver drives a red mustang convertible up a ramp and off a cliff. The car leaves the ramp at a velocity of 60 m/s at an angle of 45o to the horizontal; the cliff and ramp combined cause the car to begin its projectile motion at a height of 315m above the ground. If you were coordinating this stunt, how far away would you put a landing surface so that your stunt driver was not injured?
First let’s think about strategy. The question is basically asking how far away from the cliff the car will land. In order to find horizontal distance we need horizontal velocity and time. We can find both horizontal and vertical velocity from the initial conditions, but we’ll have to calculate the time it will take for the car to reach the ground. So first we’ll find the components of velocity:
Vx: Cos 45o = Vx/60 Vy: Sin 45o = Vy/60
60 * Cos 45o = Vx = 42.43 m/s 60 * Sin 45o = Vy = 42.43 m/s
Note: Remember that horizontal velocity is constant, but the vertical velocity we calculated above is only the initial vertical velocity.
From here we need to use the initial vertical velocity to find the time it takes the car to reach the top of its path and fall to the ground. Let’s think about this in two parts; the time it takes to reach hMAX first:
tTOP = 42.43/10 = 4.243 s
Now what about the time it takes to fall from the maximum height? Well first we need to know the maximum height:
hTOP = ½ * 10 * 4.2432 = 90.02 m
hMAX = hTOP + ho = 90.02 + 315 = 405.02 m
Now we calculate the time it takes to fall from a height of 405.02 m:
405.02 = ½ * 10 * tDOWN2
tDOWN2 = 81.004
tDOWN = 9.000 s
Putting these two times together, we have the total time it takes the car to travel up to its maximum height and then fall back down. This is the total time in the air and this is the time we will want to use to solve for horizontal distance.
tTOTAL = tTOP + tDOWN = 4.243 + 9.000 = 13.243 s
dx = 42.43 * 13.243 = 561.9 m
You will want to make sure that the landing surface is centered 561.9 m from the base of the cliff.
St. Rosemary Educational Institution. "Projectile Motion Practice & Solutions." http://schoolworkhelper.net/. St. Rosemary Educational Institution, Last Update: 2016. Web. Retrieved on: Thursday 20th October 2016. http://schoolworkhelper.net/projectile-motion-practice-solutions/.